That's the arithmetic sequence
7, 20, 33, 46, 59, 72, 85, 98, 111, 124, 137, 150
Make a new arithmetic sequence by subtracting 7 from every term:
0, 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143
Make another new arithmetic sequence by dividing every term by 13:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
The smallest possible sum represented as a sum of four distinct
numbers chosen from this sequence is 0+1+2+3 = 6
The largest possible sum represented by a sum of four distinct
numbers chosen from it is 8+9+10+11 = 38
Every integer from 6 to 38 inclusive can be represented as a sum of four distinct numbers chosen from the set {0,1,2,3,...,11
That's 38-6+1 = 33 possible sums. For every one of those sums, there is
a corresponding sum of four distinct numbers chosen from the set {7,20,33,46,...,150}?
Answer: 33 different integers can be represented as a sum of four distinct numbers chosen from the set {7,20,33,46,...,150}
Edwin